发表机构
University College London; The University of Manchester（伦敦大学学院; 曼彻斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对专家乘积高斯过程模型的后验方差高估问题，提出基于信息校准的GP-pro-c模型，在降低计算复杂度的同时，使NLL平均降2.3%、ENCE平均降12.0%，可用于高维大规模数据的贝叶斯优化。
AI 中文摘要
采用单个全局高斯过程（GP）的回归模型（GP-glo）具有三次方计算成本，限制了其对大规模数据集的可扩展性。专家乘积高斯过程模型（GP-pro）结合局部高斯过程模型以捕捉全局相关性，减轻了这种计算负担。然而，在不相交的数据子集上训练局部专家可能导致后验方差被高估。我们提出了GP-pro-c，这是一种采用基于信息的方法校准这些方差的专家乘积高斯过程模型。该方法利用高斯过程中信息增益的单调性和次模性来定义校准比率，以减小单个局部高斯过程模型的后验方差。我们使用负对数似然（NLL）、均方根误差（RMSE）和期望归一化校准误差（ENCE）对GP-pro-c进行评估。在四个合成函数和六个回归数据集上的实验表明，与未校准的GP-pro模型相比，GP-pro-c在NLL上平均降低了2.3%，在ENCE上平均降低了12.0%。所提出的方法在保持预测精度并降低计算复杂度的同时，缓解了后验方差高估的问题。GP-pro-c为可扩展高斯过程模型中的不确定性估计提供了一种有前景的方法，可作为高维大规模数据贝叶斯优化的有用代理模型。
英文摘要
Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-experts GP models (GP-pro), which combine local GP models to capture global correlations, alleviate this computational burden. However, training local experts on disjoint data subsets can lead to overestimated posterior variances. We propose GP-pro-c, a product-of-experts GP model that calibrates these variances using an information-based method. The method exploits the monotonicity and submodularity of information gain in GPs to define a calibration ratio that reduces the posterior variance of individual local GP models. We evaluate GP-pro-c using negative log-likelihood (NLL), root mean squared error (RMSE), and expected normalised calibration error (ENCE). Experiments on four synthetic functions and six regression datasets show that GP-pro-c achieves average reductions of 2.3% in NLL and 12.0% in ENCE compared with the uncalibrated GP-pro model. The proposed method mitigates posterior variance overestimation while maintaining predictive accuracy and reducing computational complexity. GP-pro-c provides a promising approach for uncertainty estimation in scalable GP models and may serve as a useful surrogate model for Bayesian optimisation with high-dimensional and large-scale data.
CommentsPublished in the Journal of Artificial Intelligence Research, Volume 86 (2026)
Journal refJournal of Artificial Intelligence Research, Vol. 86 (2026)
